本研究主要以邊界元素法計算各種柱狀幾何的熱阻問題,有包含同心圓、偏心圓、多偏心圓、正方形及多邊形幾何柱狀計算其溫度、熱通量及熱阻,由於某些幾何形狀未能有解析解,故使用邊界元素法來計算熱阻的問題,經過研究同心圓及偏心圓有解析解可對照此邊界元素法的正確性,因此經過計算後邊界元素法的數值解和解析解對應相當正確,因此可確認邊界元素法是快速、準確的一項數值解法,邊界元素法因為所計算的的點都在邊界,因此大大的減少了數值的計算量,此方法的精確度則是點數越多,越能達到要求的精度,由於邊界元素法離散誤差只產生在邊界上,因此所求的內點不可包含於邊界上的點,否則會有相當大的誤差。 經本論文之計算結果,以同心圓的熱阻為例,CASE1有相對誤差1.58%而CASE2相對誤差有1.15%,吾人做出類圓柱之熱阻表,可供工業上熱阻設計之應用需求,且此邊界元素法可推廣至其他工程之力學問題。
In this study, using the boundary element method analysis the thermal resistance of various geometries question, including concentric, eccentric, and more eccentric calculated polygonal geometry, the thermal flux and resistance, since there are some possible geometries analytical solution, the boundary element method used to calculate the thermal resistance of the problem, through research concentric and eccentric with analytical solutions can control the accuracy of the boundary element method, therefore calculated after the numerical solution of the boundary element method and the analytical solution corresponds quite right, so you can confirm the boundary element method is a fast and accurate numerical solution of a boundary element method because the calculated points are on the border, thus greatly reducing the numerical computation, the accuracy of this method is the number of points the more able to achieve the required accuracy, because the boundary element method discretization error produced only on the boundary, so the demand can not be included in the inner point on the boundary point, or there will be considerable error. In this study, the final calculation of the thermal resistance of heat flow through the path of course, is the shorter of its thermal resistance is lower, in the present study has a thermal resistance of various geometric shapes attached for reference. The results of this thesis, the thermal resistance of concentric circles for example, CASE1 a relative error of 1.58% and a relative error of 1.15% CASE2, I make a kind of resistance cylindrical form, the thermal design for industrial applications, and this boundary element method can be extended to other engineering mechanics problems.
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